Constraining dark energy from the abundance of weak gravitational lenses

Details Constraining dark energy from the abundance of weak gravitational lenses Constraining dark energy from the abundance of weak gravitational lenses

2002-10-07

arxiv.org/abs/astro-ph/0210134v1

Mon.Not.Roy.Astron.Soc. 341 (2003) 251

Astronomy and Astrophysics

Astrophysics

13 pages, 13 figures, submitted to MNRAS

Scientific paper

10.1046/j.1365-8711.2003.06421.x

We examine the prospect of using the observed abundance of weak gravitational lenses to constrain the equation-of-state parameter w of the dark energy. Here we solve the spherical-collapse model with dark energy, clarifying some ambiguities found in the literature, and provide fitting formulas for the overdensity at virialization and the linear-theory overdensity at collapse. We then compute the variation in the predicted weak-lens abundance with w. We find that the predicted redshift distribution and number count of weak lenses are highly degenerate in w and \Omega_0. If we fix \Omega_0 the number count for w=-2/3 is a factor of 2 smaller than for the \LambdaCDM model. However, if we allow \Omega_0 to vary with w such that the amplitude of the matter power spectrum as measured by COBE matches that obtained from the X-ray cluster abundance, the decrease in the predicted lens abundance is less than 25% for -1 < w < -0.4. We show that a more promising method for constraining the dark energy---one that is largely unaffected by the \Omega_0 - w degeneracy as well as uncertainties in observational noise---is to compare the relative abundance of virialized X-ray lensing clusters with the abundance of non-virialized, X-ray underluminous, lensing halos. For aperture sizes of 15 arcmin, the predicted ratio of the non-virialized to virialized lenses is greater than 40% and varies by 20% between w=-1 and w=-0.6. Overall, if all other weak lensing parameters are fixed, a survey must cover > 40 degree^2 in order for the number count to differentiate a \LambdaCDM cosmology from a w=-0.9 model to 3\sigma. However, given uncertainties in the lensing parameters, the non-virialized lens fraction provides the most robust constraint on w, requiring 50 degree^2 of sky coverage in order to differentiate w=-1 from w=-0.6 to 3\sigma.

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